The growth story in Southeast Asia appears "less shiny and glossy in bright daylight" since talk of Fed tapering began, said Leif Eskesen, HSBC's chief economist for Asean, or the Association of South East Asian Nations, in a note.

"The days of easy credit-fueled growth are behind us," he said. "Growth will be more difficult to come by in coming years. An important reason for this is that growth has relied too much on cheap credit up until now, which has built up leverage a bit too fast," he said.

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The Asean-five, or Malaysia, Thailand, Indonesia, Philippines and Vietnam, need to do the "heavy lifting" of economic reforms to make the region "the serious alternative to China and India that we think it deserves to be," he added, noting it's important to start reforms soon as it will take time for their positive impact on growth to be felt.

In some countries, such as Thailand, challenges from aging demographics in coming years could dampen growth if they aren't countered with reforms, Eskesen said.

Each country has its own structural issues, many centering on infrastructure needs, education and the labor market, he noted. Several also need to bring down fiscal deficits to make way for more productive spending, he said.

"The sharp fall in external demand during the global financial crisis led policy makers in the region to turn towards domestic demand as an engine of growth. However, this boost to domestic demand was driven largely by expansionary monetary and fiscal policies and hence lacked a productive dynamic," Morgan Stanley said in a note last week.

"Productivity will have to do the heavy lifting in this cycle to lift growth," it said.

But Morgan Stanley doesn't expect the region's productivity to get a fillip from a strong revival in export growth, despite an improving developed market economic outlook, as the re-industrialization of the U.S. economy will present increasing headwinds. It noted the region's export levels have been fairly steady over the past three years.